Is there a way to create an executable of a game not version specific?
The standard copies of blender that you download include both blender and blenderplayer which is a game engine only runtime. Blender includes the "Save As Game Engine Runtime" addon that gives you an export to runtime option. There is an explanation of creating a standalone runtime in the manual. There is also a "Game Engine Publishing" addon to help export for multiple platforms.

YoFrankie was released 9th December 2008 with blender 2.48a. When blender 2.50 was released a year later the python API was changed dramatically and has no compatibility with previous versions. YoFrankie contains many python scripts that would need to be re-written to work in anything newer than 2.49. Some of the character rigs and animations would also need some adjustment to work in newer versions. As all of the scripts and data files are available someone could update the game to a newer version but so far no-one has made the effort.